Question

4log(0,1) x=1g(0,1) 2+log(0,1)8

Answer 1

4log(0,1) x=1g(0,1) 2+log(0,1)8;
Основание логарифма равно (0,1), однако один из слагаемых логарифма имеет основание 10(0.1)=1 (1g z =1og(10) z ). 
Из определения о логарифме мы можем знать, что основание логарифма  больше 0 и не равно 1. Значит в большой вероятности в учебнике опечатка.
Если это так, то запись будет таковой:
4log(0,1) x=1og(0,1) 2+log(0,1)8;
Используя формулу rlog(s) x = log(s) x^r, получаем:
log(0,1) x^4=1og(0,1) 2х8;
log(0,1) x^4=1og(0,1) 16;
Опускаем логарифм с одинаковым основанием, оставляя только следующее выражение:
 x^4= 16;
x=2.

Answer 2

I can help you solve this logarithmic equation. First, let me rewrite it using the common logarithm base 10:

4log(0.1)x = log(0.1)2 + log(0.1)8

Using the properties of logarithms, I can simplify the right-hand side as follows:

log(0.1)2 + log(0.1)8 = log(0.1)(2×8) = log(0.1)16

Now, I can use the change of base formula to convert the logarithms with base 0.1 to base 10:

log(0.1)x = log10(x) / log10(0.1)

log(0.1)16 = log10(16) / log10(0.1)

Substituting these expressions into the original equation, I get:

4(log10(x) / log10(0.1)) = log10(16) / log10(0.1)

Multiplying both sides by log10(0.1), I get:

4log10(x) = log10(16)

Dividing both sides by 4, I get:

log10(x) = log10(16) / 4

Using the property of logarithms that says loga(b) = c if and only if a^c = b, I can write:

x = 10^(log10(16) / 4)

Using a calculator, I can evaluate the right-hand side as:

x ≈ 0.6325

Therefore, the solution of the logarithmic equation is x ≈ 0.6325.

You can check this answer by plugging it back into the original equation and verifying that both sides are equal.

If you want to learn more about logarithms and how to solve logarithmic equations, you can visit some of the web pages I found for you . I hope this helps!